Equuleus is the second smallest constellation in
the Northern Hemisphere, tucked between the head of
Pegasus and the dolphin,
Delphinus. There is no certain legend applied
to Equuleus and it is supposedly created by the second-century Greek
astronomer Ptolemy because it was added to his Algamest, though
according to Geminos (130 - 60 B.C.) it was created by Hipparchos
(Hipparchus), the Greek astronomer who lived around
190-120 B.C. Hipparchus mapped the position of 850 stars in the earliest
known star chart. His observations of the heavens form the basis of
Ptolemy's geocentric cosmology [AHD] [Allen argues on p.218 of Star
Names that because Ptolemy did not mention the star near the south pole,
Achernar, that his catalogue was
not based upon original observations, but drawn from the now lost catalogue
of Hipparchos]. Hipparchos is also credited with discovering the precession
of the equinoxes, or as Allen believes (p.209), may have been merely
the publisher of that discovery made by the Egyptians, or perhaps adopted
by them from Chaldaea.

Equuleus is the head of a horse with a flowing mane
which the Arabs called AlFarasalAwwal,
'the First Horse', in reference to its rising before
Pegasus. Ptolemy called it Ippou
Protome; Ippou, or hippo, is Greek for horse.
Greek protome means head or bust (in sculpture), with later
astronomers it was Equus primus and prior. The image is traditionally
a figure of a horse or foal, said to represent either Celeris,
the brother of Pegasus, given by Mercury to Castor (Ovid, Met.,
xii. 408); or Cyllarus, given to Pollux by Juno, (Virgil,
Geor., iii. 90). Others say he was Pegasus' offspring and a flying
colt, or the creature struck by Neptune's trident from the earth when
contesting with Minerva for superiority of Athens.

Hevelius, Firmamentum, 1690, depicts the head of
Aquarius (Ganymedes) encroaching onto the
heads of the two horses; Pegasus and
Equuleus. A Homer poem tells how Ganymedes was carried
off by Zeus and to compensate the father of Ganymedes, King Laomedon
of Troy, Zeus gave him two horses [1].

Klein
supplies more cognates to *kel-3': acolyte (one who assists the celebrant in the performance
of liturgical rites, from Greek akholouthos, a- +keleuthos is cognate with Lithuanian kelias, 'way',
keliauju, 'I journey', from Indo-European base *qeleu-,
enlargement of *qel-, *kel-, 'to drive', whence Latin
celer, 'swift'), clonus (from the Greek for
'violent, confused motion', is a series of involuntary muscular contractions
due to sudden stretching of the muscle), hodden (a
coarse kind of cloth made of undyed wool, in Scotland), holt
(lair of an animal), proceleusmatic (a metrical foot
of four short syllables, from Greek prokeleusmatikos, 'to give
orders before', from keleuein, to rouse to action. "The ancient
proceleusmatic song by which the rowers of galleys were animated may
be supposed to have been of this kind." [Samuel Johnson
3]).

"Some of the mythologists said that the constellation represented
... the creature struck by Neptune's (Poseidon) trident from the
earth when contesting with Minerva (Athena) for superiority" (over
Athens. See that myth below). [Allen,
Star Names].

Or it could be the foal (Equuleus is also said to be a foal) Rhea
tricked Cronus into swallowing as a substitute for their son Poseidon
(an aspect of Poseidon)? Poseidon is said to have invented horse racing.
Horses were sacrificed in his honor [7].
"Some storytellers insisted he invented the horse by smashing his trident
down upon a rock. In any case, it is said that he invented horse racing"
[8]
Pegasus was a son of Poseidon because he
mated with the Gorgon Medusa in that form.

"Poseidon was a son of Cronus and Rhea. In most accounts, he
is swallowed by Cronus at birth. However in some versions of the
story, he, like his brother Zeus, did not share the fate of his
other brother and sisters who were swallowed by Cronus. He was saved
by his mother Rhea who tricked Cronus into eating a foal instead,
saying that she had given birth to a horse. Poseidon was raised
by the Telchines on Rhodes, just as Zeus was raised
by the Korybantes on Crete" [9].

The myths associated with Equuleus

"Some of the mythologists said that the constellation represented
the creature struck by Neptune's (Poseidon) trident from the earth when
contesting with Minerva (Athena) for superiority" [Allen,
Star Names]:

"Athena (Minerva) became the patron goddess of the city of Athens,
in a competition with Poseidon (Neptune). They agreed that each
would give the Athenians one gift and the Athenians would choose
whichever gift they preferred. "Neptune struck the ground with his
trident and there sprang forth a horse. The gods were filled with
wonder at the sight of the noble animal, and when Neptune explained
how useful it would be to man, they all thought that the victory
would be his. Minerva then produced an olive tree; at this all the
gods laughed with scorn, but when the goddess, heedless of their
laughter, had explained how all its parts--the wood, the fruit,
and the leaves--could be used by man, how it was the sign of peace
while the horse was the symbol of war, they decided that Minerva
had won, and since her name among the Greeks was Athene, she gave
to the city the name of Athens".
http://www.sacred-texts.com/time/smd/smd13.htm

There might be a connection between the Greek words; polis,
city, and polos, foal:

This horse is also said to be Cyllarus (Greek
Kullaros), given by Mercury to Castor of whom
Ovid describes:

"[In the battle of the Kentauroi and Lapithes:] Nor did his beauty
ransom [centaur] Cyllarus, fighting that day, if
hybrids such as he be granted beauty. His beard was just beginning,
a golden beard, and golden tresses fell down on his shoulders reaching
to his flanks. High-mettled grace shone in his face; his neck, chest,
shoulders, hands and every manly part seemed like a sculptor’s much-praised
masterpiece. Unblemished too his equine shape, nor less fine than
his man’s. With horse’s head and neck he’s make fit mount for Castor,
so high stood his chest-muscles, so rideable his back. Jet black
he was, the whole of him, save that his tail was white and legs
were milk-white too. Many a centauress would be his mate, but one
had gained his heart, [she-centaur] Hylonome. In the high woods
there was none comelier of all the centaur-girls, and she alone
by love and love’s sweet words and winning ways held Cyllarus,
yes, and the care she took to look her best (so far as that may
be with limbs like that). She combed her glossy hair, and twined
her curls in turn with rosemary or violets or roses, and sometimes
she wore a pure white lily. Twice a day she bathed her face in the
clear brook that fell from Pagasae’s high forest, twice she plunged
her body in its flow, nor would she wear on her left side and shoulder
any skin but what became her from best-chosen beasts. Their love
was equal; on the hills they roamed together, and together they
would go back to their cave; and this time too they went into the
Lapithae’s palace side by side and side by side were fighting in
the fray. A javelin (no knowing from whose hand) came from the left
and wounded Cyllarus, landing below the place where
the chest joins neck – slight wound, but when the point was pulled
away, cold grew his damaged heart and cold his limbs. Hylonome embraced
him as he died, caressed the wound and, putting lips to lips, she
tried to stay his spirit as it fled. And when she saw him lifeless,
she moaned words that in that uproar failed to reach my ears; and
fell upon the spear that pierced her love, and, dying, held her
husband in her arms." - Ovid, Metamorphoses 12.210
http://www.theoi.com/Georgikos/KentaurisHylonome.html

In myth the Gemini Twins ride two horses
"the immortal steeds Cyllarus and Harpagus" [2].
It seems that Equuleus is Cyllarus, and Harpagus must
be Pegasus.

The two centaur horses, Cyllarus and his wife
Hylonome,
might relate to these two adjacent constellations Equuleus and
Pegasus. Cyllarus is identified with
Equuleus. Hylonome 'browser of the woods', is from
the district Pagasae, similar to 'pegasus', and 'pagan' etc. (from the
root *pag-
as explained on the Pegasus page).

Equuleus, the Foal that modern Latin critics would turn into
Eculeus, lies half-way between the head of
Pegasus and the Dolphin (Delphinus),
marked by the trapezium of 4th- to 5th-magnitude stars, — alpha, beta,
gamma, and zeta, — although Argelander catalogues nine others,
and Heis twelve down to 6.7 magnitude. Thus "the flaming {Page 213}
shoulders" of our motto are lacking here, and the reference may be to
Pegasus, to which the characterization certainly is more appropriate.

The Germans call it Fullen, the Filly, and
Kleine Pferd, which with us is the Little Horse,
the French Petit Cheval, and the Italian Cavallino.

Hood wrote of it about 1590:

This constellation was named of almost no writer, saving
Ptolomee and Alfonsus who followith Ptolemy, and therefore
no certain tale or historic is delivered thereof, by what means
it came into heaven; but we know that Geminos mentioned it as having
been formed by Hipparchos, its stars till then lying in the early
Dolphin. Still Hipparchos did not allude to it in his Commentary,
nor did Hyginus, Manilius, or Vitruvius, a century after him.

Ptolemy catalogued it as Ippou Protome, this last
word equivalent to our Bust for the upper part of an animal figure;
but with later astronomers it was Equusprimus and
prior, as preceding Pegasus in rising;
while from its inferior size come our own title and Equulus,
Equiculus, and EquusMinor. Gore's translation
of I'AstronomicPopulaire, following Proctor,
has Equus, the larger Horse being Pegasus.

Ptolemy's idea of the incompleteness of the figure was repeated in
the Equi Sectio, Equi Praesectio,
Sectio equina, Sectio Equi minoris,
Semi-perfectus, and Praesegmen of
various authors and Latin versions of the Syntaxis and of the
AlfonsineTables; the Almagest of 1551 gave
Praecisio Equi.

Chrysococca's Tables had Kephale Ippou,
the EquiCaput of some Latin writers, and the Horse’sHead of our day.

The Arabians followed Ptolemy in calling it AlKitahalFaras, Part of a Horse, Chilmead's Kataat
Alfaras; AlFarasalThani, the Second
Horse, alluding either to its inferior size, or to the time of its adoption
as a constellation; and AlFarasalAwwal,
the First Horse, in reference to its rising before
Pegasus. From the first of these comes the
modem Kitalpha (Kitalpha
is the alpha star), sometimes applied to the constellation, and generally
to the brightest star. Riccioli's ElmacAlcheras certainly
is a barbarism, — not unusual, however, with him; but La Lande's rarely
used Hinnulus, a Young Mule, has more to commend it.

With the Hindus it was another of their Acvini, the Horsemen,
although their figuring resembled ours.

Some of the mythologists said that the constellation represented
Celeris, the brother of Pegasus,
given by Mercury to Castor; or
Cyllarus, given to Pollux by
Juno; or the creature struck by Neptune's trident from the earth when
contesting with Minerva for superiority; but it also was connected {Page
214} with the story of Philyra and Saturn. Caesius, in modern times,
associated it with the King’s Horse that Haman hoped
for, as is told in the BookofEsther; and
Julius Schiller, with the Rosa mystica.